Viscoelastic damping devices are effective in mitigating vibrations experienced by Civil Engineering structures subjected to natural actions, such as earthquakes, wind gusts or ocean waves. In this paper, an efficient computational framework for non-classically damped viscoelastic structures is proposed, allowing rheological information on nano-reinforced elastomeric devices to be incorporated in the time-domain dynamic analysis of structures equipped with such components. For thiss purpose, the Generalized Maxwell (GM) model and the Laguerre’s polynomial approximation (LPA) can be effectively adopted to represent the relaxation function of the viscoelastic materials, leading to an enlarged state-space model. It is also shown that these models can be used beyond the linear range, provided that the strain-dependent values of their mechanical parameters are identified.